Block #149,832

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 9/4/2013, 3:01:18 PM · Difficulty 9.8580 · 6,653,501 confirmations

TWN

Bi-Twin Chain

Interleaved pairs of primes that differ by 2, forming twin prime pairs at each level.

Block Header

Block Hash

9a6246e18c75952a28deac1bfe77c5d1db75f7b5b11b7e2bed313906d4b23089

View on Chainz ↗

Height

#149,832

Difficulty

9.857984

Transactions

Size

1.05 KB

Version

Bits

09dba4df

Nonce

117,919

Timestamp

9/4/2013, 3:01:18 PM

Confirmations

6,653,501

Mined by

⛏️ P2SHAP9mkN5CvZv9yJumdWwandb1esCp9EUL1P

Merkle Root

5e9d2e65bfa1072599796a825ca147c4f4677fa05eef45ae7dbf14365d366196

Transactions (3)

Coinbase737b4be343c9d9…ece6fc2a106724

1 in → 1 out10.2900 XPM109 B

AP9mkN5C…Cp9EUL1P

53e5e1b7041ac4…362f7e5391d73f

2 in → 2 out20.6000 XPM307 B

AFz9fXym…wh4UqpkL AVPoJqux…uwMeTPGo

7c1f517f40040d…68fef5b0c82df3

4 in → 2 out31.0300 XPM571 B

AHnvJDiF…j8QVpNpY AHd84rb7…WMojsZ6S

Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) — it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

2.822 × 10⁹³(94-digit number)

28226328600502329736…00865526297070687879

Discovered Prime Numbers

Lower: 2^k × origin − 1 | Upper: 2^k × origin + 1

These are the actual prime numbers discovered by this block, computed using the verified Primecoin formula. Each number has been independently confirmed to pass the Fermat primality test. Use the FactorDB links to verify any number independently.

Level 0 — Twin Prime Pair (origin ± 1)

origin − 1

2.822 × 10⁹³(94-digit number)

28226328600502329736…00865526297070687879

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.822 × 10⁹³(94-digit number)

28226328600502329736…00865526297070687881

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: origin + 1 − origin − 1 = 2 (twin primes ✓)

Level 1 — Twin Prime Pair (2^1 × origin ± 1)

2^1 × origin − 1

5.645 × 10⁹³(94-digit number)

56452657201004659473…01731052594141375759

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.645 × 10⁹³(94-digit number)

56452657201004659473…01731052594141375761

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^1 × origin + 1 − 2^1 × origin − 1 = 2 (twin primes ✓)

Level 2 — Twin Prime Pair (2^2 × origin ± 1)

2^2 × origin − 1

1.129 × 10⁹⁴(95-digit number)

11290531440200931894…03462105188282751519

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.129 × 10⁹⁴(95-digit number)

11290531440200931894…03462105188282751521

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^2 × origin + 1 − 2^2 × origin − 1 = 2 (twin primes ✓)

Level 3 — Twin Prime Pair (2^3 × origin ± 1)

2^3 × origin − 1

2.258 × 10⁹⁴(95-digit number)

22581062880401863789…06924210376565503039

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.258 × 10⁹⁴(95-digit number)

22581062880401863789…06924210376565503041

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^3 × origin + 1 − 2^3 × origin − 1 = 2 (twin primes ✓)

Level 4 — Twin Prime Pair (2^4 × origin ± 1)

2^4 × origin − 1

4.516 × 10⁹⁴(95-digit number)

45162125760803727578…13848420753131006079

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 consecutive prime numbers forming a Bi-Twin Chain. The prime chain origin — the large number shown above — anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

★☆☆☆☆

Rarity

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

How Primecoin's Proof-of-Work Constructs These Primes

Primecoin stores a value called the prime chain origin in each block. The miner found a large integer such that when divided by a primorial (the product of small primes: 2 × 3 × 5 × 7 × …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial — that divisibility is part of the proof.

Prime Chain Origin = First Prime × Primorial (2·3·5·7·11·…)

Source: Primecoin prime.cpp — CheckPrimeProofOfWork()

This is why the origin has many small prime factors — those factors are the primorial divisor. The chain then extends from the first prime using the TWN formula:

TWN: twin pairs (p, p+2) where p = origin/primorial − 1 and p+2 = origin/primorial + 1

Cross-reference on Chainz Explorer